Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x-5y &= 1 \\ 4x+4y &= 8\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $4y = -4x+8$ Divide both sides by $4$ to isolate $y$ $y = {-x + 2}$ Substitute this expression for $y$ in the first equation. $-2x-5({-x + 2}) = 1$ $-2x + 5x - 10 = 1$ Simplify by combining terms, then solve for $x$ $3x - 10 = 1$ $3x = 11$ $x = \dfrac{11}{3}$ Substitute $\dfrac{11}{3}$ for $x$ back into the top equation. $-2( \dfrac{11}{3})-5y = 1$ $-\dfrac{22}{3}-5y = 1$ $-5y = \dfrac{25}{3}$ $y = -\dfrac{5}{3}$ The solution is $\enspace x = \dfrac{11}{3}, \enspace y = -\dfrac{5}{3}$.